## Convergence of vector spherical wave expansion method applied to near-field radiative transfer |

Optics Express, Vol. 19, Issue S4, pp. A772-A785 (2011)

http://dx.doi.org/10.1364/OE.19.00A772

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### Abstract

Near-field radiative transfer between two objects can be computed using Rytov’s theory of fluctuational electrodynamics in which the strength of electromagnetic sources is related to temperature through the fluctuation-dissipation theorem, and the resultant energy transfer is described using the dyadic Green’s function of the vector Helmholtz equation. When the two objects are spheres, the dyadic Green’s function can be expanded in a series of vector spherical waves. Based on comparison with the convergence criterion for the case of radiative transfer between two parallel surfaces, we derive a relation for the number of vector spherical waves required for convergence in the case of radiative transfer between two spheres. We show that when electromagnetic surface waves are active at a frequency the number of vector spherical waves required for convergence is proportional to *R _{max}
*/

*d*when

*d/R*→ 0, where

_{max}*R*is the radius of the larger sphere, and

_{max}*d*is the smallest gap between the two spheres. This criterion for convergence applies equally well to other near-field electromagnetic scattering problems.

© 2011 OSA

**OCIS Codes**

(030.5620) Coherence and statistical optics : Radiative transfer

(240.6690) Optics at surfaces : Surface waves

(260.2160) Physical optics : Energy transfer

(290.4020) Scattering : Mie theory

(290.4210) Scattering : Multiple scattering

(290.6815) Scattering : Thermal emission

**ToC Category:**

Radiative Transfer

**History**

Original Manuscript: May 9, 2011

Revised Manuscript: May 26, 2011

Manuscript Accepted: May 27, 2011

Published: June 6, 2011

**Virtual Issues**

Vol. 6, Iss. 8 *Virtual Journal for Biomedical Optics*

**Citation**

Karthik Sasihithlu and Arvind Narayanaswamy, "Convergence of vector spherical wave expansion method applied to near-field radiative transfer," Opt. Express **19**, A772-A785 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-S4-A772

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